Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices

We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on the lattice, characterising the pretails of eventually periodi...

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Bibliographic Details
Published in:arXiv.org 2012-05
Main Authors: Baake, Michael, Neumaerker, Natascha, Roberts, John A G
Format: Article
Language:English
Subjects:
Automorphisms
Lattices
Orbits
Toruses
Online Access:Get full text
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Summary:We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on the lattice, characterising the pretails of eventually periodic orbits. Next we study the nature of the symmetries and reversing symmetries of toral automorphisms on a given lattice, which has particular relevance to (quantum) cat maps.
ISSN:2331-8422
DOI:10.48550/arxiv.1205.1003